On first looking into Brébeuf's Lucan

Georges de Brébeuf not only translated Lucan's Pharsalia in rhyming alexandrines but also produced a travesty of the same work. This unique situation can be understood as a complicated response to the aesthetic provocation offered by the Latin poem. Translation and travesty form a hybrid whole. It is argued that our encounter with Brébeuf’s contradictory poet can help us to better grasp what kind of writer Lucan is: one who grotesquely undercuts his own sublime aspirations

An introduction to Mandelbrot cascades

In this course, we propose an elementary and self-contained introduction to canonical Mandelbrot random cascades. The multiplicative construction is explained and the necessary and sufficient condition of non-degeneracy is proved. Then, we discuss the problem of the existence of moments and the link with nondegeneracy. We also calculate the almost sure dimension of the measures. Finally, we give an outline on multifractal analysis of Mandelbrot cascades. This course was delivered in september 2013 during a meeting of the "Multifractal Analysis GDR" (GDR no 3475 of the french CNRS).Comment: 36 page

On measures driven by Markov chains

We study measures on $[0,1]$ which are driven by a finite Markov chain and which generalize the famous Bernoulli products. We propose a hands-on approach to determine the structure function $\tau$ and to prove that the multifractal formalism is satisfied. Formulas for the dimension of the measures and for the Hausdorff dimension of their supports are also provided

Rayleigh-Benard stability and the validity of quasi-Boussinesq or quasi-anelastic liquid approximations

The linear stability threshold of the Rayleigh-Benard configuration is analyzed with compressible effects taken into account. It is assumed that the fluid obeys a Newtonian rheology and Fourier's law of thermal transport with constant, uniform (dynamic) viscosity and thermal conductivity in a uniform gravity field. Top and bottom boundaries are maintained at different constant temperatures and we consider here boundary conditions of zero tangential stress and impermeable walls. Under these conditions, and with the Boussinesq approximation, Rayleigh (1916) first obtained analytically the critical value 27pi^4/4 for a dimensionless parameter, now known as the Rayleigh number, at the onset of convection. This manuscript describes the changes of the critical Rayleigh number due to the compressibility of the fluid, measured by the dimensionless dissipation parameter D and due to a finite temperature difference between the hot and cold boundaries, measured by a dimensionless temperature gradient a. Different equations of state are examined: ideal gas equation, Murnaghan's model and a generic equation of state, which can represent any possible equation of state. We also consider two variations of this stability analysis. In a so-called quasi-Boussinesq model, we consider that density perturbations are solely due to temperature perturbations. In a so-called quasi-anelastic liquid approximation, we consider that entropy perturbations are solely due to temperature perturbations. In addition to the numerical Chebyshev-based stability analysis, an analytical approximation is obtained when temperature fluctuations are written as a combination of only two modes. This analytical expression allows us to show that the superadiabatic critical Rayleigh number quadratic departure in a and D from 27pi^4/4 involves the expansion of density up to the degree three in terms of pressure and temperature.Comment: 42 pages, 30 figures, 4 table

Measures and the Law of the Iterated Logarithm

Let m be a unidimensional measure with dimension d. A natural question is to ask if the measure m is comparable with the Hausdorff measure (or the packing measure) in dimension d. We give an answer (which is in general negative) to this question in several situations (self-similar measures, quasi-Bernoulli measures). More precisely we obtain fine comparisons between the mesure m and generalized Hausdorff type (or packing type) measures. The Law of the Iterated Logarithm or estimations of the L^q-spectrum in a neighborhood of q=1 are the tools to obtain such results.Comment: 18 page

Second Order Topological Superconductivity in π\pi-Junction Rashba Layers

We consider a Josephson junction bilayer consisting of two tunnel-coupled two-dimensional electron gas layers with Rashba spin-orbit interaction, proximitized by a top and bottom $s$-wave superconductor with phase difference $\phi$ close to $\pi$. We show that, in the presence of a finite weak in-plane Zeeman field, the bilayer can be driven into a second order topological superconducting phase, hosting two Majorana corner states (MCSs). If $\phi=\pi$, in a rectangular geometry, these zero-energy bound states are located at two opposite corners determined by the direction of the Zeeman field. If the phase difference $\phi$ deviates from $\pi$ by a critical value, one of the two MCSs gets relocated to an adjacent corner. As the phase difference $\phi$ increases further, the system becomes trivially gapped. The obtained MCSs are robust against static and magnetic disorder. We propose two setups that could realize such a model: one is based on controlling $\phi$ by magnetic flux, the other involves an additional layer of randomly-oriented magnetic impurities responsible for the phase shift of $\pi$ in the proximity-induced superconducting pairing

Raison pratique et information asymétrique : Pour une éthique de la communication dans un monde risquophobe

Dans leur tentative de justifier moralement une « bonne » décision, les grandes théories de l’éthique normative ignorent des paramètres incontournables de la prise de décision. Or une classe importante de jeux non-coopératifs étudie plus spécialement les effets de ces paramètres sur la prise de décision des agents. Il s’agit des jeux à information asymétrique avec modèle agent-principal. Cet article se propose donc, dans la première partie, de voir comment opère la rationalité de l’agent quand on intègre ces paramètres. La deuxième partie soulignera les conséquences qui émanent de cette conception « élargie » de la rationalité sur le plan éthique et politique